In how many ways can 4 letters be selected an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The word $MATHEMATICS$ contains $11$ letters: $M, M, A, A, T, T, H, E, I, C, S$. There are $3$ pairs of identical letters $(M, A, T)$ and $5$ dist

Vedclass · Accepted Answer

$2454$

Vedclass · Answer

(D) The word $MATHEMATICS$ contains $11$ letters: $M, M, A, A, T, T, H, E, I, C, S$. There are $3$ pairs of identical letters $(M, A, T)$ and $5$ distinct letters $(H, E, I, C, S)$.Case $I$: Two letters of one kind and two of another kind.Number of ways $= ^3C_2 	imes \frac{4!}{2!2!} = 3 	imes 6 = 18$.Case $II$: Two letters of one kind and two distinct letters.Number of ways $= ^3C_1 	imes ^7C_2 	imes \frac{4!}{2!} = 3 	imes 21 	imes 12 = 756$.Case $III$: All four letters are distinct.Number of ways $= ^8C_4 	imes 4! = 70 	imes 24 = 1680$.Total number of arrangements $= 18 + 756 + 1680 = 2454$.

In how many ways can $4$ letters be selected and arranged from the word $MATHEMATICS$?

Similar Questions

If $7 \cdot ^nP_3 = 20 \cdot ^{n+1}P_2$,then $n = \dots$

$S_1, S_2, \ldots, S_{10}$ are the speakers in a conference. If $S_1$ addresses only after $S_2$,then the number of ways the speakers address is

Find the value of $n$ such that $^{n}P_{5} = 42 \, ^{n}P_{3}$,where $n > 4$.

How many even numbers of $3$ different digits can be formed from the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ (repetition is not allowed)?

If all permutations of the letters of the word $MASK$ are arranged in the order as in a dictionary,with or without meaning,which one of the following is the $19^{th}$ word?

Vedclass Test Series

Exam Paper Generator

Online Exam Module